The word "פּלשׁת (pelesheth)" appears in the Bible eight times. It is translated either as "Palestina/Palestine" or "Philistia/Philistine" as follows:
Translating as "Palestine" is justified by the Hebrew. Hebrew words originally had only consonants without vowels, so a word could have been pronounced in various ways depending on dialect or age. The consonants of the Hebrew word "פּלשׁת (P.L.S.Th.)" could have vowels added and transliterated as either "P.a.L.e.S.Th. (hence, Palestine)" or "P.h.i.L.i.S.Th. (hence, Philistia)". The issue depends on whether the Pe has a dagesh or not (פּ or פ), whether it is a Sin (שׂ) or a Shin (שׁ), and what vowels are placed in between the consonants. The Masoretic dots are not the only ways to pronounce Hebrew words. "Palestine" is just as valid a transliteration as "Philistia". Even if we take the Masoretic pronunciation of "pelesheth" at face value, it is disingenuous to say that it must be translated as "Philistia" and not as "Palestina" given that "Palestina" is closer phonetically to the Masoretic Hebrew. The modern Palestinian movement was not known to the KJV translators in 1611. However, it is due to the historical identification of the region occupied by the Philistines as "Palestina" (a Latin transliteration of the Semitic name) that the modern Palestinian movement derived its name.
As for consistency, it appears the KJV translates "פּלשׁת" as "Palestina/Palestine" when it is referring to the geographical region whereas it translates "פּלשׁת" as "Philistia/Philistine" when it is referring to the nationality (the people). It is clear that in Exodus 15:14 and Joel 3:4, "פּלשׁת" is referring to the geographical region as opposed to the nationality. Isaiah 14:29 and Isaiah 14:31 might appear at first to refer to the nationality, but the context of Isaiah 14:31 ("Howl, O gate; cry, O city; thou, whole Palestina,") shows that a geographical reference is in view. This is made clearer by the phrase "whole Palestina", which mirrors phrases such as "the whole land" or "the whole earth" appearing throughout the Old Testament which refer to the entirety of geographical areas. It is clear that in Psalm 60:8, Psalm 83:7, and Psalm 108:9, "פּלשׁת" is referring to the nationality (the people). Perhaps the controversial one is Psalm 87:4 because "Philistia" is used even though the context seems to be listing and referring to geographical locations. However, upon closer reading there seems to be a personification of these geographical locations. God gets their attention, saying to them, "behold". Egypt is listed by its emblematic name "Rahab" which is literally a "sea monster" (Brown-Driver-Briggs' Hebrew Definitions). The referenced entities in Psalm 87:4 are not so much geographical locations as they are the national consciousness of those nations - which are the people.
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